We were up that way when I was 20 weeks pregnant. We spent a great day on the beach at Cape Tribulation, at the time the longer walk was closed for works but it was just lovely wandering along the beach. We also loved walking through Mossman Gorge, it was beautiful in there and not too strenuous as there was a shorter loop for if you got tired and a longer loop for if you wanted to keep going.
Have a great time, I wish I was going again